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Some New Random Field Tools for Spatial Analysis Robert J. Adler

Summary: Some New Random Field Tools for Spatial Analysis
Robert J. Adler
Abstract This is a brief review, in relatively non-
technical terms, of recent rather technical advances in the
theory of random field geometry. These advances have
provided a collection of explicit new formulae describ-
ing mean values of a variety of geometric characteristics
of excursion sets of random fields, such as their volume,
surface area and Euler characteristics. What is particu-
larly important in these formulae is that whereas the pre-
vious theory covered only stationary, Gaussian random
fields, the new theory requires neither stationarity nor, a
fortiori, isotropy. Furthermore, it covers a wide class of
non-Gaussian random fields. The formulae provided by
these advances have a wide range of potential applica-
tions, including new techniques of parameter estimation,
model testing, and thresholding for spatial and space-
time functions. The paper reviews this theory, and pro-
vides brief descriptions of some of the applications.
Key words: Random field, excursion set, nodal domain,


Source: Adler, Robert J. - Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology


Collections: Mathematics; Engineering